This volume, honoring over forty years of Miklos Csorgo's work in probability and statistics, reflects the state of current research. It offers a comprehensive collection of surveys introducing new results with complete proofs and expository papers giving an historic overview. Contributions were made by an international group of experts.The book covers the following topics: path properties of stochastic processes, probability theory with applications, complete convergence of renewal counting processes and bootstrap means, weak convergence of random size sums, almost sure stability of weighted maxima, procedures for detecting changes in statistical models, statistical inference via conditional quantiles, cumulative sums, multinomial samples, empirical processes, applications to economics, and self-normalized partial sums processes. The section, 'Applications to Economics', deals primarily with applications of stochastics to financial time series models. The book is suitable for graduate students and researchers interested in probability theory, stochastic processes, mathematical statistics, and applications of these mathematical/statistical sciences.
Path properties of stochastic processes: Our joint work with Miklos Csorgo by E. Csaki, A. Foldes, and Z. Shi Brownian sheet and quasi-sure analysis by D. Khoshnevisan Hardy's inequality in $L^2([0,1])$ and principal values of Brownian local times by G. Peccati and M. Yor Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge by G. Peccati and M. Yor Tell me the values of a Wiener at integers, I tell you its local time by P. Revesz Probability theory with applications: Chaotic maps with slowly decaying correlations and intermittency by R. J. Bhansali, M. P. Holland, and P. S. Kokoszka Recent results on $p$-stable convex compact sets with applications by Y. Davydov and V. Paulauskas Convex rearrangements of random elements by Y. Davydov and R. Zitikis Hierarchical random walks by D. A. Dawson, L. G. Gorostiza, and A. Wakolbinger On Helgason's number and Khintchine's inequality by K. A. Ross and Q.-M. Shao Complete convergence of renewal counting processes and bootstrap means: Convergence rates and precise asymptotics for renewal counting processes and some first passage times by A. Gut and J. Steinebach On the complete convergence of bootstrap means by S. Csorgo Weak convergence of random size sums, almost sure stability of weighted maxima: Weak convergence of random sums and maximum random sums under nonrandom norming by I. Cwiklinska and Z. Rychlik Criteria for the almost sure stability of weighted maxima of bounded i.i.d. random variables by R. J. Tomkins Procedures for detecting changes in statistical models: Permutation principle and bootstrap in change point analysis by M. Huskova Change point detection based on $L$-statistics by E.-E. A. A. Aly Sequential tests for change in the parameters of nested random effects model by E. Atenafu and E. Gombay Using U-statistics based processes to detect multiple change-points by M. Orasch Statistical inference via conditional quantiles, cumulative sums, multinomial samples, and empirical processes: Statistical methods learning and conditional quantiles by E. Parzen Testing regression models: A strong martingale approach by M. D. Burke Conditional distribution of the H-coefficient in nonparametric unfolding models by A. R. Dabrowski and H. Dehling Empirical processes based on pseudo-observations II: The multivariate case by K. Ghoudi and B. Remillard Applications to economics: Probabilistic and statistical properties of GARCH processes by I. Berkes, L. Horvath, and P. Kokoszka Stochastic finance: Discrete time processes and risk neutral pricing by R. Kulperger Estimating the correlation of processes using extreme values by D. L. McLeish Analyzing residual processes of (G)ARCH time series models by H. Yu Self-normalized partial sums processes: On weighted approximations and strong limit theorems for self-normalized partial sums processes by M. Csorgo, B. Szyszkowicz, and Q. Wang On Darling-Erdos type theorems for self-normalized sums by Q. Wang.